How long is a coastline?

Pick one piece of coast. The three panels show it far away, closer, then closest. Each closer look reveals smaller bends the faraway view hid.

A measuring stick is straight. Tap it onto the bend: it can touch at both ends, but it cannot curl into the bay between them.

tap to lay down the stick

This long ruler touches two gold landing points. A shorter ruler would make the same end-to-end walk in shorter hops. Neither total has been measured yet.

One long coral ruler bridges a deep blue bay between two gold landing points.

Same coast. Same method. Different hop sizes.

First, walk one fixed ruler around the island. Drag from START to FINISH. Each coral line is one straight ruler step.

ruler steps placed0

startfinish

Undo the drag and the ruler walks backward.

Nia will measure the same coast again with a much shorter ruler. Same start. Same finish. Same careful method.

Matching coast panels hold one long ruler and one short ruler at the same gold starting point.

Will the measured total stay put?

Same coast. Same careful measuring. Only the ruler changes.

As the ruler gets shorter and shorter, what happens to the measured length?